T47:02 731 VPN 97% 5 TOⓇ + : 6. Find the natural cubic spline to approximate...
T47:02 731 VPN 97% 5 TOⓇ + : 4. Find the Hermite interpolating polynomial which interpolates the values f(1) = 4, f'(1) = -3, f(4) = 13, f'(4) = 9 and verify your answer. 5 13
its a numerical analysis question QUESTION 4 (a) A natural cubic spline that fits the data given by (10) f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) z+ y = 9, 1² + y2 = 25, 2, y > 0. Perform one iteration of Newton's method to approximate the solution,...
5. (a) The natural spline S(a) passing through the n+ points is a collection of n cubic functions S,(x) defined in the n intervals x, Sxx Suppose that all the points are equally spaced, with uniform point spacing h=5m-x, for jso,1,..,,n. Ifthe symbols M,, 0, represent the second derivatives of the spline at cach of the mesh points, show that in each intervl-.R-1 For the natural cubic spline (for which M, O and M-=0 ), show that the moments M...
Find the natural cubic spline interpolant to f(x) = e^(x^3) at the nodes {xi} i=0 = {−2, 0, 2} . Calculate the value of the interpolant at x = 1. What is the error at this point?
0.19 0.. 1. (Natural Splines) Find the natural cubic spline S(x) satisfying S(0) = 0, S(1/2) = 1, S(1) = 0. Your answer will be 2 cubic polynomials, S.(x), S1(x). Verify that your answer satisfies all the necessary conditions (interpolation, continuity of 1st and 2nd derivatives, boundary conditions). We were unable to transcribe this image
6. (20) Consider the table X 02 3 y = f(x) 7 11 -4 (a) Fit the given data with a quadratic spline. (b) Find an approximate value of f(3) using the first-degree spline. 6. (20) Consider the table X 0 | 2 | y = f(x) | 7 11 | 3 5 (a) Fit the given data with a quadratic spline. YE (b) Find an approximate value of f (3) using the first-degree spline.
help wanted?? thank you explain correctly Problem 1 Use the trapezoidal rule technique to approximate the following integrals: a) 「(x2+1)dr(Note: use 0.5 increments forx) b) sina d INote: use a MATLAB function to subdivide the interval into eight equal parts) c e dx (Note: use 0.25 increments for x Problem 2 Use the Simpson's rule to evaluate the following integrals aDdr Problem 3: Given the polynomial: x3-6x2 + 30-0, Use MATLAB to find all roots of this polynomial. Use MATLAB's...
please determine the output in a simple form #include <stdio.h> 2 3 //Item 02 4 int main() 5 6 7 8 9 10 int i for( i = 0 ; i < 5 ; i++ ) ifo 12 13 14 15 16 17 18 19 20 21 printf("A" printf("B"); if i > 2 ) printf("C"); 23 24 25 26 27 28 29 30 31 32 if( i 3) printf( "D") if>4) printf("E 34 35 36 37 38 39 40 41...
Lupter 12 The Metric System 97 the basic unit, writing them in small letters without a period. An exception to this rule is the abbreviation for mi crogram. Because the letters mg stand for milligram, microgram is abbreviated as yg or meg.) The abbreviation for kilograms is kg, the abbreviation for milligrams is mg, and the abbreviation for milli liter is ml. The abbreviation mL is increasingly being used for milliliter and is the abbreviation used in this book. Although...
(**) In #5-#6, find all solutions of under determined linear system by using the row operations: (2. 0:01 (0.21 -4.02 +2.13 +24 +02 -13 +2.04 +0.02 +0x3 +344 = 11 = 5 = 9 2 0.0 ( 0.1 +2.02 +02 0.02 -13 -4.03 0.13 +0.04 +3.25 +0.04 +45 + +2:05 = 7 = -1 = 1